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    Coursera
    1. Discrete Math and Analyzing Social Graphs
    2. Week 3
    3. Finding probabilities using rules
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    Finding probabilities using rules

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    1.
    Question 1

    L​et AAA and BBB be some events defined on the same probability space. Assume we know that P(A)=1/2P(A)=1/2P(A)=1/2, P(B)=1/3P(B)=1/3P(B)=1/3 and P(A∪B)=2/3P(A\cup B)=2/3P(A∪B)=2/3. Find P(A∩B)P(A\cap B)P(A∩B) (as a proper fraction).

    1 / 1 point
    16\frac{1}{6}61​
    1 / 6
    Check
    Correct

    A​ccording to rule of sum of probabilities, P(A∪B)=P(A)+P(B)−P(A∩B)P(A\cup B)=P(A)+P(B)-P(A\cap B)P(A∪B)=P(A)+P(B)−P(A∩B). Therefore, P(A∩B)=P(A)+P(B)−P(A∪B)=1/2+1/3−2/3=1/6P(A\cap B) = P(A) + P(B) - P(A\cup B)=1/2 + 1/3 - 2/3=1/6P(A∩B)=P(A)+P(B)−P(A∪B)=1/2+1/3−2/3=1/6.

    2.
    Question 2

    A​ fair dice rolled three times. What is the probability that "6" occurred at least once during this rollings?

    1 / 1 point
    91216\frac{91}{216}21691​
    1-125/216
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    Correct

    Complement event is "6" never occurred. Its probability is 53/635^3/6^353/63. The probablity of our event is 1−53/63=91/2161-5^3/6^3=91/2161−53/63=91/216.